Pair of Linear Equations in Two Variables Class 10 Mcq Test (100301)

Graphically, the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0  represents two lines which are:

(a) intersecting at exactly one point       

(b) intersecting at exactly two points  

(c) coincident

(d) parallel

The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has: 

(a) many solutions

(b) no solution

(c) one solution

(d) 2 solutions

The pair of equations x = 0 and x = 7 has:

(a) two solutions

(b) no solution

(c) infinitely many solutions

(d) one solution

The pair of linear equations x – 2y = 0 and 3x + 4y = 20 have: 

(a) one solution

(b) two solutions 

(c) many solutions

(d) no solution

The value of k for which the system: 

4x + 2y = 3, (k – 1)x – 6y = 9

has no unique solution is:

(a) –13

(b) 9

(c) –11

(d) 13

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16, represent coincident lines?

(a) \(1\over 2\)

(b) \(-1\over 2\)

(c) 2

(d) − 2

The sum of the digits of a two-digit number is 9. If 27 is added to it, digits of the number get reversed. The number is:

(a) 63

(b) 72

(c) 81

(d) 36 

In the equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), if \({\frac{a_1}{a_2}}\ne{\frac{b_1}{b_2}}\), then the equations will represent:

(a) coincident lines

(b) parallel lines

(c) intersecting lines

(d) none

If a pair of linear equations is consistent, then the lines will be:

(a) always intersecting

(b) always coincident

(c) intersecting or coincident

(d) parallel

The pair of equations 5x – 15y = 8 and \(3x-9y=\frac{24}{5}\) has:  

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution